Anisotropic Fokker‐Planck Models for the Evolution of Globular Star Clusters: The Core‐Halo Connection

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Abstract
We present the results of direct Fokker-Plank simulations of the dynamical evolution of a cluster of identical stars that undergoes core collapse followed by a binary-driven reexpansion phase, including a careful treatment of the effects of velocity-space anisotropy. We have substantially refined the two-dimensional Fokker-Planck code first developed by Cohn to improve the energy conservation by a factor of about 100 and to include energy input from binaries produced by three-body interactions. The treatment of anisotropy allows us to construct realistic models for the evolution of global structure, including the development of a halo by ejection of mass from the central regions. We have focused on the evolution of an isolated cluster, with no tidal boundary, in order to provide a benchmark for comparison with simulations that include tidal mass loss. The overall evolution of the central regions of the cluster resembles that of isotropic Fokker-Planck models, with strongly nonlinear core oscillations observed for total star number N>104. However, radial-orbit-dominated anisotropy becomes significant within the central regions during core collapse phases and is present at large amplitude in the halo at all times. The outer regions of the cluster expand much more rapidly than is observed in isotropic simulations, with the expansion of the radius containing 90% of the cluster mass strongly accelerating at the time of the first core collapse. There is close agreement between the expansion observed here and that seen in the shorter duration direct N-body integrations for N~104 reported by Spurzem & Aarseth and Makino. In contrast, the halo expansion that we observe is more rapid than that seen in the somewhat lower resolution anisotropic Fokker-Planck simulations reported by Takahashi. Our simulations indicate a close connection between the collapsed core and the outer halo: frequent stellar encounters in the dense core rapidly boost stars to large orbital apocenter distances on highly elongated, low angular momentum orbits. These orbits provide an efficient energy and mass transport conduit between the inner and outer regions. This process may lead to more rapid globular cluster dissolution in the Galactic tidal field than had previously been inferred in recent studies based on isotropic Fokker-Planck models.